Given: m arc IV =140°, m arc VK =30°, m∠ISV=135° Find: m∠VPL

Accepted Solution

Answer:[tex]m<VPL=80\°[/tex]Step-by-step explanation:step 1Find the measure of arc PKwe know thatThe measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.Letx------> the measure of arc IVy ------> the measure of arc PK[tex]m<ISV=\frac{1}{2}(x+y)[/tex]substitute the values and solve for y[tex]135\°=\frac{1}{2}(140\°+y)[/tex][tex]270\°=(140\°+y)[/tex][tex]y=270\°-140\°=130\°[/tex]The measure of arc PK is [tex]130\°[/tex]step 2Find the measure of angle VPLwe know thatThe inscribed angle measures half that of the arc comprisingLetz------> the measure of arc VKy ------> the measure of arc PK[tex]m<VPL=\frac{1}{2}(z+y)[/tex]substitute the values[tex]m<VPL=\frac{1}{2}(30\°+130\°)=80\°[/tex]